[PD] Colored (fractal, 1/f^a) noise generator for PD

Martin Peach martin.peach at sympatico.ca
Sun Aug 20 23:56:00 CEST 2006


Mathieu Bouchard wrote:
> On Sun, 20 Aug 2006, Charles Henry wrote:
>
>> 1/f^a noise is a fractal because it is self similar under different 
>> size windows. 1/(kf)^a = 1/k^a * 1/f^a, so the magnitude of spectrum 
>> viewed over a different window is just scaled by a certain 
>> amplitude.  The same applies to the time domain as well (but it has 
>> to be interpreted as a probability function).
>
> Then by this standard, the 1/x function is self-similar, and so are 
> all hyperbolas. That is, as long as similarity is defined as modulo 
> the group of diagonal matrices conjugated by rotation matrices.
>
I don't see that. Zooming in and out of 1/x or a hyperbola just makes 
the curve look bigger or smaller, whereas noise looks the same at all 
scales.

> Isn't the definition of fractal requiring some kind of noninteger 
> Hausdorff dimension?
>
 From B. Mandelbrot, The Fractal Geometry of Nature, Freeman, 1983, p.15:
"A fractal is by definition a set for which the Hausdorff Besicovitch 
dimension strictly exceeds the topological dimension"
"Every set with a noninteger D is fractal"
"However, a fractal may have a noninteger D ... the trail of Brownian 
motion is fractal because D=2, while Dt = 1" (i.e. a randomly meandering 
line will eventually completely fill a plane)

Martin



>  _ _ __ ___ _____ ________ _____________ _____________________ ...
> | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
> | Freelance Digital Arts Engineer, Montréal QC Canada
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